ORI GIN AL PA PER

Modelling Estuarine Biogeochemical Dynamics: Fromthe Local to the Global Scale

Pierre Regnier • Sandra Arndt • Nicolas Goossens • Chiara Volta •

Goulven G. Laruelle • Ronny Lauerwald • Jens Hartmann

Received: 5 December 2012 / Accepted: 26 November 2013� Springer Science+Business Media Dordrecht 2013

Abstract Estuaries act as strong carbon and nutrient filters and are relevant contributors

to the atmospheric CO2 budget. They thus play an important, yet poorly constrained, role

for global biogeochemical cycles and climate. This manuscript reviews recent develop-

ments in the modelling of estuarine biogeochemical dynamics. The first part provides an

overview of the dominant physical and biogeochemical processes that control the trans-

formations and fluxes of carbon and nutrients along the estuarine gradient. It highlights the

tight links between estuarine geometry, hydrodynamics and scalar transport, as well as the

role of transient and nonlinear dynamics. The most important biogeochemical processes

are then discussed in the context of key biogeochemical indicators such as the net eco-

system metabolism (NEM), air–water CO2 fluxes, nutrient-filtering capacities and element

budgets. In the second part of the paper, we illustrate, on the basis of local estuarine

modelling studies, the power of reaction-transport models (RTMs) in understanding and

quantifying estuarine biogeochemical dynamics. We show how a combination of RTM and

high-resolution data can help disentangle the complex process interplay, which underlies

the estuarine NEM, carbon and nutrient fluxes, and how such approaches can provide

integrated assessments of the air–water CO2 fluxes along river–estuary–coastal zone

Electronic supplementary material The online version of this article (doi:10.1007/s10498-013-9218-3)contains supplementary material, which is available to authorized users.

P. Regnier (&) � N. Goossens � C. Volta � G. G. Laruelle � R. LauerwaldDepartment of Earth and Environmental Sciences, Universite Libre de Bruxelles, Brussels, Belgiume-mail: pregnier@ulb.ac.be

S. ArndtBRIDGE, School of Geographical Sciences, University of Bristol, Bristol, UK

R. LauerwaldCNRS, FR636, Institut Pierre-Simon Laplace, 78280 Guyancourt Cedex, France

J. HartmannInstitute for Biogeochemistry and Marine Chemistry, KlimaCampus, Universitat Hamburg, Hamburg,Germany

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continua. In addition, trends in estuarine biogeochemical dynamics across estuarine

geometries and environmental scenario are explored, and the results are discussed in the

context of improving the modelling of estuarine carbon and CO2 dynamics at regional and

global scales.

Keywords Reactive-transport models � Land–ocean continuum � Carbon

cycle � CO2 � Estuaries � Biogeochemistry

1 Introduction

Situated at the transition between freshwater and marine environments, estuaries are key

components of the land–ocean aquatic continuum. They act as strong nutrient and carbon

filters and are relevant contributors to the atmospheric CO2 budget (e.g. Smith and Hol-

libaugh 1993; Cai and Wang 1998; Wollast 1998; Rabouille et al. 2001; Borges and

Frankignoulle 2002; Borges 2005; Zhai et al. 2005; Laruelle et al. 2010; Borges and Abril

2011; Mackenzie et al. 2011, Laruelle et al. 2013; Regnier et al. 2013). Along the estuarine

gradient, oceanic and terrestrial carbon and nutrient inputs are modified by biogeochemical

processes, buried in sediments, incorporated into biomineralized structures or, in the case

of gaseous species such as CO2, exchanged with the atmosphere. All these transformations

are driven by a complex interplay between geological, physical, chemical and biological

processes, which are modulated by a wide array of forcing mechanisms, such as wind

stress, light, water temperature, waves, tides or freshwater discharge.

The estuarine biogeochemical dynamics, the lateral carbon and nutrient fluxes and the

vertical air–water gaseous exchange are characterized by strong spatial gradients from the

tidally dominated mouth to the river-dominated upstream reaches. A pronounced temporal

variability ranging from hours (e.g., tidal forcing) to months (e.g., discharge, seasonal

temperature), and longer (e.g., historical nutrient loading) is another distinct feature of

estuarine systems. Human activities, in particular, have changed both the quantity and

quality of terrestrial carbon and nutrient fluxes to estuaries and the coastal ocean with

likely consequences for global biogeochemical cycles and climate (Ver et al. 1999; Rab-

ouille et al. 2001; Mackenzie et al. 2004; 2011, Regnier et al., 2013). However, the

quantitative significance of the estuarine bioreactor as a regulator of land–ocean carbon

and nutrient fluxes or global atmospheric CO2 concentrations remains poorly constrained

(e.g. Borges et al. 2005; Mackenzie et al. 2005; Regnier et al. 2013). This limited quan-

titative understanding mainly results from the inherent spatial and temporal variability of

the estuarine environment that is difficult to resolve on the basis of observations alone.

Observations only provide instantaneous and localized information that cannot easily be

extrapolated to the scale of the entire estuarine system. Yet, important whole system

properties, such as the net ecosystem metabolism (NEM, Borges and Abril 2011) and the

estuarine-filtering capacity (Nixon et al. 1996), require spatially integrated assessments at a

high temporal resolution over a seasonal or annual cycle (e.g. Arndt et al. 2009).

Reaction-transport models (RTMs) provide ideal tools to resolve the variability inherent

in the estuarine environment. RTMs are used as analogues of the real world. Such models

are based on a process–functional approach that focuses on energy and matter fluxes, and

treats the biogeochemical system as a bioreactor (Haag and Kaupenjohann 2000). RTMs

are generally developed to investigate the transport and transformation of a selected set of

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constituents in a compartment of the Earth system. Albeit commonly used in the fields of,

for example, early diagenesis or groundwater research (Lichtner et al. 1996), the concept

has rarely been applied in estuarine and ocean science. Nevertheless, many biogeochemical

models developed in these fields are fully consistent with the above definition.

RTMs complement field observations, because their integrative power provides the

required extrapolation means for a system-scale analysis (e.g. Arndt and Regnier 2007;

Arndt et al. 2009) over the entire spectrum of changing forcing conditions, including the

long-term response to land-use and climate change (Paerl et al. 2006; Thieu et al. 2010).

Over the last 3 decades, RTM approaches have increasingly been used to unravel the

biogeochemical dynamics of estuarine systems, including studies on water quality, phy-

toplankton and bacterial dynamics or elemental mass budgets (e.g. O’Kane 1980; Soetaert

and Herman 1995; Lee et al. 2005; Lin et al. 2007; Arndt et al. 2009; Baklouti et al. 2011;

Gypens et al. 2012). Furthermore, the mechanistic understanding gained through these

RTM studies allows to identify the important processes and forcings that drive the cycling

of bioactive elements. They thus have the potential to provide important guidelines for the

design of global biogeochemical models (e.g. Falkowski et al. 2000; Mackenzie et al.

2011). However, even today, only a few modelling studies incorporate the full suite of

interacting physical, biological and chemical processes controlling the coupled transfor-

mations of carbon and nutrients along an estuarine gradient (e.g. Cloern 2001; Tappin et al.

2003; Hofmann et al. 2008a). Estuarine modelling studies are also clearly biased towards

anthropogenically impacted systems in industrialized countries such as the East Coast of

the USA, Western Europe and Australia (e.g. Cerco and Cole 1993; Regnier and Steefel

1999; Cerco 2000; Billen et al. 2001; Kim and Cerco 2003; Margvelashvili et al. 2003;

Tappin et al. 2003; Robson and Hamilton 2004, 2008; Scavia et al. 2006; Shen 2006; Wild-

Allen et al. 2009; Cerco et al. 2010). Although data availability for other regions is steadily

increasing, model applications to estuaries located in Siberia, Alaska, Southeast Asia, the

Hudson Bay or along the tropical Western Atlantic are missing (Fig. 1).

Our ability to assess the quantitative role of the estuarine environment for global bio-

geochemical cycles and greenhouse gas budgets, as well as its response to on-going land-

use and climate changes, requires comparative studies that cover a large range of different

systems, thus enabling the identification of global patterns (Borges and Abril 2011).

However, model applications are currently limited by data requirements for calibration and

validation, as well as by the high computational needs required to address physical, bio-

geochemical and geological processes at the relevant temporal and spatial scales. This

computational barrier is rapidly exacerbated when seasonal and inter-annual timescales

need to be jointly resolved. Therefore, the application of two- or three-dimensional estu-

arine RTMs generally remains restricted to short simulation timescales (\1 year) and well-

known systems for which detailed bathymetric and geometric information is available

(Fig. 1). Such two- or three-dimensional RTMs have been set up for, among others, the

Chesapeake Bay (Cerco and Cole 1993; Cerco and Noel 2004; Cerco et al. 2010), the Pearl

Estuary (Guan et al. 2001; Zhang and Li 2010), the St. Lawrence Estuary (Benoit et al.

2006; Lefort et al. 2012) and the Scheldt Estuary (Vanderborght et al. 2007; Arndt and

Regnier 2007; Arndt et al. 2009). One-dimensional RTMs are computationally less onerous

than multi-dimensional approaches. Yet, their application also remains restricted to indi-

vidual estuarine systems (e.g. O’Kane 1980; Garnier et al. 1995, 2007; Hanley et al. 1998;

Billen et al. 2001, 2009; Vanderborght et al. 2002; Macedo and Duarte 2006; Even et al.

2007a, b; Hofmann et al. 2008a, b), partly because regional- and global-scale simulations

are currently compromised by the limited availability of comprehensive data sets.

Therefore, the development of scaling approaches including new modelling tools that

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extrapolate knowledge from well-studied to data-poor estuarine systems is required to

advance our quantitative understanding of their role in the global climate system.

In this contribution, we review the most important estuarine physical and biogeo-

chemical processes that govern the transformations of carbon and nutrients along the

estuarine gradient. We then illustrate, on the basis of examples of local estuarine modelling

studies, how RTMs can be used to quantify estuarine budgets, fluxes and filtering

capacities. The linkages and interactions between the river network, the estuarine envi-

ronment and the coastal zone are also briefly analysed. Next, we show how a combination

of reaction-transport modelling and high-resolution data can help disentangle the complex

process interplay that underlies the estuarine NEM, greenhouse gas fluxes and C-filtering

capacities. This approach is then generalized to assess the response of these key biogeo-

chemical indicators to changes in estuarine geometry for different environmental scenarios

assuming typical Western European climate conditions. Finally, the results are discussed in

the context of the development of mechanistically rooted upscaling strategies, from the

local to the regional scale and beyond.

2 Estuaries Within the Context of the Land–Ocean Continuum

The land–ocean aquatic continuum is commonly defined as the interface, or transition

zone, between terrestrial ecosystems and the open ocean (Billen et al. 1991; Mackenzie

et al. 2011; Regnier et al. 2013). Estuaries are integral part of this continuum, but their

Fig. 1 Location of published estuarine biogeochemical model applications (n = 99). Red: tidal systems(type 2; n = 74); Blue: other types (n = 25) in the classification of Durr et al. (2011). Watershedshighlighted in grey correspond to tidal systems. Small and big dots correspond to 1 and 1–5 modelapplications; circles correspond to more than 5 model applications. The bar charts represent the distributionof model dimensions (top) and model span (bottom). Steady-state (orange) and transient (black) simulationsare reported separately

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spatial boundaries are often difficult to delineate without ambiguity (Elliott and McLusky

2002). Although estuaries may comprise coastal environments as diverse as deltas, lagoons

and fjords, our analysis exclusively focuses on tidal systems due to their intense biogeo-

chemical processing and long residence times (e.g. Wollast 1983). In addition, tidal

estuaries generally reveal a sharp salinity gradient, thus facilitating model calibration and

validation using specific methods that are not easily applicable to other coastal systems.

Tidal estuaries, referred to as type 2 in the typology of Durr et al. (2011), account for a

total surface area of 276 X 103 km2 and 27 % of the world’s exorheic freshwater water

discharge (Laruelle et al. 2013). Together with large rivers, they are the main conduits

through which freshwater is delivered to the sea. They also receive a significant fraction of

the global carbon and nutrient load from terrestrial ecosystems. According to the analysis

of the GlobalNEWS2-project (Seitzinger et al. 2005; Mayorga et al. 2010), tidal systems

receive total organic carbon, nitrogen and phosphorus loads of 81, 12 and 0.7 Tg year-1

(an equivalent of 25, 34 and 32 % of the global land to ocean fluxes), respectively.

A tidal estuary can be geographically divided into the freshwater tidal river, the brackish

to saline estuary and the area of the coastal ocean that is under the direct influence of the

estuarine plume (Fig. 2). The freshwater part can often be further divided into a pre-

oxygen minimum zone and an oxygen minimum zone, where a significant proportion of the

terrestrial and riverine matter is processed (e.g. Vanderborght et al. 2002; Amann et al.

2012). As an example, the three major zones are illustrated in Fig. 2 for the Delaware and

Scheldt watersheds. Their tidal intrusion length and thus the landward extension of the

estuarine environment are highly variable as they depend on the amplitude of the tidal

wave at the estuarine mouth, the estuarine geometry and the upstream river discharge. In

the Delaware and Scheldt watersheds, the estuaries typically extend 170 and 215 km

inwards, respectively. The average freshwater residence time is about 60–90 days in the

Scheldt (Wollast and Peters 1978) and 80 days in the Delaware estuary (Fisher et al. 1988),

but can vary significantly in response to changes in the freshwater discharge.

Most tidal estuaries are alluvial estuaries, which, from a morphological point of view,

are geologically young environments. They are characterized by movable beds and a

measurable influence of freshwater discharge. Alluvial estuaries develop in sediment

deposits delivered by the river and the sea, as opposed to fixed bed estuaries, which are

remnants of an older geological period. In alluvial estuaries, the tidal discharge directly

depends on the channel size. In turn, the water movement, driven by the tides and the

freshwater discharge, leads to a redistribution of the unconsolidated sediments, which

shapes the estuary (Savenije 2005). This co-adjustment results in a dynamic equilibrium

that allows deriving hydraulic information from the estuarine shape and vice versa. Thus,

although alluvial estuaries cover a wide variety of shapes, their geometries reveal common

characteristics (Savenije 1992). The estuarine cross-sectional area and width typically

decrease exponentially with distance from the mouth. The cross-section and width con-

vergence lengths, defined as the distance between the mouth and the point at which the

cross section or width is reduced to 37 % of its value at the mouth, are directly related to

the dominant hydrodynamic forcing. A high river discharge typically induces a prismatic

channel with long convergence lengths, while a large tidal range results in a funnel-shaped

estuary with short convergence lengths. For example, the Scheldt and the Delaware are

typical tidally dominated, funnel-shaped alluvial estuaries, occasionally referred to as

marine-dominated estuaries (Jiang et al. 2008), with a cross-section convergence length of

only 26 and 41 km and a width convergence length of 28 and 42 km, respectively

(Savenije 1992). Their width at the mouth is 15 km for the Scheldt and 38 km for the

Delaware (Savenije 1992), and their average water depth is *10 m (Canuel et al. 2012).

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At the other end of the spectrum of shapes, the Solo or the Lalang are typical examples of

fluvial-dominated, prismatic alluvial estuaries that are also referred to as river-dominated

estuaries (Jiang et al. 2008). Their cross-section convergence lengths are 226 and 217 km,

while their width convergence lengths are 226 and 96 km, respectively (Savenije 2005).

Within the estuarine reactor, large riverine fluxes of terrestrial or fossil dissolved and

particulate organic matter mix with organic matter derived from marine sources or pro-

duced in situ (Heip and Herman 1995; Frankignoulle et al. 1998; Abril et al. 2002). This

organic carbon is, together with large land-derived nutrient fluxes, biogeochemically

modified along the estuarine gradient before it is ultimately exported to the adjacent coastal

zone (Hedges and Keil 1999; Middelburg and Herman 2007; Arndt et al. 2011; Amann

et al. 2012). At decadal scales, process rates vary due to changes in the catchment area or

anthropogenic activities (e.g. Thieu et al. 2010, 2011). In a pristine watershed, for example,

the major source of organic carbon is the top soil and the vegetation (Mulholland 1997;

Gueguen et al. 2006; Lauerwald et al. 2012). The input of dissolved inorganic carbon,

mainly carbonate alkalinity, is controlled by chemical rock weathering and thus the

lithology (Meybeck 1993; Cai et al. 2008; Moosdorf et al. 2011). Land-use substantially

affects carbon and nutrient exports from watersheds (Fig. 2). In agricultural areas, the

application of fertilizer is the major non-point source of nutrients in surface water (Billen

et al. 2009). Soil erosion plays a key role in mobilizing particulate organic carbon and

phosphorus from the terrestrial to the aquatic system (Beusen et al. 2005; Quinton et al.

2010; Regnier et al. 2013). Furthermore, anthropogenic point sources of reactive nutrients

and labile organic carbon can have significant effects on the biogeochemistry of rivers and

Fig. 2 The Delaware (a) and Scheldt (b) estuaries in the context of the land–ocean continuum. Black linesdelineate the watersheds. White dashed line: estuarine mouth; black dashed line: upper limit of the tidalriver. Land-use data were derived from the GlobCover data set (Arino et al. 2007). Information about inlandwater bodies and marsh areas was taken from ESRI (2006, http://www.esri.com/data/find-data) and theCorine Land Cover data set. The watersheds of the Delaware and Scheldt rivers are dominated by forests andagricultural land, respectively. Both watersheds are influenced by extensive urban areas, although theirspatial distribution is contrasted. Tidal marsh areas are still abundant in the Delaware estuary, while only asingle patch is present along the Scheldt estuary. Permanent web source for Corine data: http://www.eea.europa.eu

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estuaries (Vanderborght et al. 2002; Mackenzie 2013). Enhanced weathering due to

application of lime or rock powder to adjust soil pH causes increased alkalinity fluxes and

dissolved inorganic carbon fluxes (Hartmann and Kempe 2008; Raymond et al. 2008).

3 The Estuarine Filter

3.1 Physics

The dynamic interplay between tidal forcing and freshwater inflow is the fundamental

driver of estuarine hydrodynamics. It induces not only a strong spatial variability in the

flow and transport properties, but also significant temporal fluctuations with characteristic

timescales ranging from turbulent eddies lasting minutes to the semi-diurnal or diurnal

tides, and finally the residual (long-term) circulation displaying spring–neap, seasonal and

yearly cycles (O’Kane and Regnier 2003). Although the spatial and temporal aspects of the

estuarine dynamics are discussed separately here, it should be emphasized that they are

intimately linked.

3.1.1 Spatial Variability

The hydrodynamic and biogeochemical properties display a dominant spatial variability

along the estuarine axis that is generally stronger than the cross-sectional variability

(O’Kane and Regnier 2003). Because of this characteristic, a one-dimensional represen-

tation of the estuarine physics often provides a representation of the main hydrodynamic

and solute transport properties that is suitable for a quantitative description of the estuarine

biogeochemistry (Uncles and Radford 1980; Friedrichs and Aubrey 1988; Regnier et al.

1998).

The superposition of fluvial and tidal influences causes important longitudinal variations

in energy dissipation, divergence of the energy flux, distortion of the tidal wave and

salinity (e.g. Jay et al. 1990; Dalrymple et al. 1992; Arndt et al. 2007). This supports a

division of the estuarine environment into a tidally dominated zone and a river-dominated

zone, separated by an intermediate zone, where tidal and fluvial energy influence are of

similar magnitude (Jay et al. 1990; Dalrymple et al. 1992). Figure 3 illustrates the profiles

of energy dissipation, tidal amplitude and salinity along the estuarine axis. Two alluvial

estuaries, characterized by a different dominant hydrodynamic forcing and, thus, different

shapes, are considered: a tidally dominated, funnel-shaped estuary and a fluvial-dominated,

prismatic estuary. This conceptual sketch shows that the extension of the different estu-

arine zones strongly depends on the relative importance of tidal and fluvial energy. A

dominant tidal influence generally results in a funnel-shaped estuary that is characterized

by a strong channel convergence, i.e. a short convergence length and a long salt intrusion

length (Savenije 2005). In these systems, the strong convergence of the estuarine banks

leads to an amplification of the tidal wave in the downstream part of the estuary where

mechanical energy is almost exclusively provided by the tides. The flux divergence of the

tidal energy is also balanced by dissipation at the estuarine bottom (Dyer 1995; Arndt and

Regnier 2007). Energy dissipation increases in upstream direction due to channel con-

vergence and the associated increase in tidal amplitude. The strong tidal influence coun-

teracts the residual downstream transport of salt and maintains small salinity gradients in

the lower estuary. Salinity intrudes far upstream in the estuary through dispersion and tidal

pumping, and the salt intrusion length equals about two-third of the total estuarine length

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(Savenije 2005). Further upstream, convergence becomes small, and the influence of the

river discharge increases progressively. The tidal influence is significantly reduced by

friction, and energy dissipation is controlled by the fluvial energy flux towards the sea (e.g.

Giese and Jay 1989, Horrevoets et al. 2004). The respective areas of dominant tidal and

fluvial energy dissipation are separated by a zone of minimum energy dissipation, the so-

called balance point, where both contributions are of similar but low magnitude (Jay et al.

1990; Dalrymple et al. 1992). A strong fluvial influence, on the other hand, results in

prismatic systems with a low channel convergence (i.e. long convergence length) and a

sharp salinity gradient over a short distance. The long convergence length, as well as the

dominant river discharge, results in a rapid dampening of the tidal wave upstream. Salinity

decreases rapidly within the estuary because the residual downstream transport is signif-

icantly larger than the dispersive transport. Energy dissipation, on the other hand, steadily

increases upstream where the dominant fluvial energy results in maximal energy dissipa-

tion (Giese and Jay 1989).

Although the spatial variability along the curvilinear axis of the estuary is generally

dominant, smaller cross-sectional variability in hydrodynamics may become important for

suspended particulate matter (SPM) or phytoplankton distributions, especially for systems

displaying complex coastline configurations and irregular bathymetries. Such morpho-

logical features may induce significant cross-sectional and vertical gradients that cannot be

resolved in a one-dimensional framework. They thus limit the quantification of processes

Fig. 3 Longitudinal distribution of tidal energy (a, b), tidal amplitude (c, d) and salinity (e, f) for a tidallydominated estuary (left) and a fluvial-dominated estuary (right)

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such as primary production (e.g. Cloern 1996, 1999), sorption onto solid particles or

bottom-water hypoxia. For instance, the deep trench in the centre of the Chesapeake Bay

determines the longitudinal and lateral extent of hypoxia of bottom waters during the

summer (Cerco 2000). Bottom friction and wind may also induce significant vertical

variations in the current field, as in the Pamlico Sound estuarine system (Lin et al. 2007).

Furthermore, the benthic biogeochemical dynamics often reveal a marked two-dimensional

pattern (e.g. Arndt and Regnier 2007) as a result of widely varying local hydrodynamic

conditions between shallow intertidal flats, characterized by conditions of low kinetic

energy and net SPM deposition, and deep tidal channels where net erosion prevails. A

complex circulation is also often observed at the transition between the outer estuary and

the coastal zone. Examples of such a transition zone include the Cape Fear River Estuary

(e.g. Lin et al. 2008), the Seine plume (Cugier et al. 2005), the Scheldt Estuary (Arndt et al.

2011), the Chesapeake Bay (Cerco 2000) or the Bay of Brest (Laruelle et al. 2009a).

3.1.2 Temporal Variability

Estuaries are inherently dynamic systems that are characterized by nonlinearities in flow

and material transport, as well as important departures from steady state (e.g. Regnier et al.

1997; Uncles and Stephens 1999; Dyer 2001; Arndt et al. 2009). The transient nature of the

estuarine environment can be illustrated by examining the relationship between salinity

and river discharge (Fig. 4a). If the estuary is in a time-invariant state, the seaward

advection of salt exactly balances the landward dispersion of salt (Bowden 1963). In this

case, the river discharge unambiguously determines the salinity for any given cross section

along the estuarine gradient (Regnier et al. 1998). Therefore, differences between observed

pairs of river–discharge–salinity values and the theoretical steady-state relationship (solid

curve in Fig. 4a) serve as a ‘measure’ of the departure from steady state (e.g. Officer and

Lynch 1981). For a passive tracer, the time required for the estuarine system to adjust to

fluctuating boundary conditions (weeks to months) is much larger than the characteristic

timescales of these fluctuations (days to a few weeks). The resulting time lags create the

observed departures from steady state (Fig. 4a) and can lead to a significant transient mass

storage (or depletion) within the estuary. This is also true for reactive species, for which the

interplay between transient mass storage and production/consumption processes can lead to

complex seasonal dynamics (see, for instance, Sect. 4.2.1 and Fig. 7).

The generation of low-frequency components by nonlinear interactions among tidal

constituents also leads to significant fluctuations in the residual (long-term) water flow.

This effect can be of sufficient magnitude and persistence to exert a significant influence on

the residence time and, thus, on the biogeochemical transformations within the estuary

(e.g. Regnier et al. 1998; Arndt et al. 2009). The relative magnitude of these nonlinear

interactions depends on the physical characteristics of the estuary and the external forcings

(Parker 1991). Figure 4b illustrates snapshots of the departure of the residual cross-sec-

tional water flow from the mean river discharge along the gradient of a macro-tidal estuary

for different discharge conditions. The difference between residual water flow and mean

river discharge is maximal close to the estuarine mouth and decreases with an increase in

fluvial influence upstream. Although the difference is most pronounced under low to

average discharge conditions, it is still noticeable under high discharge conditions. The

tidally induced fluctuations in the residual transport field can even result in a landward

residual water flow if low river discharge coincides with a spring tide (Regnier et al. 1998).

Such dynamics have been reported for numerous estuaries (e.g. Uncles and Jordan 1980;

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Sommerfield and Wong 2011) and have important implications for the quantification of

biogeochemical processes and export fluxes of C and nutrients.

3.2 Biogeochemistry

The most important biogeochemical processes that determine estuarine biogeochemical

dynamics are represented schematically in Fig. 5. Here, their significance for key bio-

geochemical indicators (NEM, estuarine carbon dioxide fluxes and nutrient-filtering

capacity) and elemental budgets is discussed.

3.2.1 Biogeochemical Processes

Organic matter (CH2O in Fig. 5) plays a key role in the biogeochemical dynamics of

estuarine systems, because the production and degradation of organic carbon exert an

important influence on almost all biogeochemical variables. Estuaries receive a complex

mix of organic matter from very different sources as reflected by their characteristic d13C

and D14C profiles between the river and marine end-members (e.g. Middelburg and Her-

man 2007). Large amounts of allochthonous terrestrial or fossil organic matter are exported

from land by rivers and groundwater. In addition, rivers may carry significant amounts of

labile organic matter from anthropogenic sources, for instance, sewage (Mackenzie et al.

2011). Along the estuarine gradient, this allochthonous organic matter is mixed with

autochthonous organic matter produced by phytoplankton or intertidal vegetation and,

further downstream, with allochthonous marine organic matter imported from the coastal

ocean through tidal pumping (Bianchi 2007). While the amount of allochthonous material

brought into the estuary is essentially controlled by transport, the contribution of

autochthonous material to the estuarine organic matter pool is determined by the difference

between rates of net primary production (NPP), phytoplankton (Phy) mortality and sub-

sequent decomposition (Fig. 5).

In estuarine environments, NPP strongly depends on the interplay between water col-

umn turbidity, nutrient availability and the flushing rate of estuarine waters that control the

residence time of phytoplankton in the system (Cloern et al. 1983). In addition,

Fig. 4 a Salinities at a fixed location along the longitudinal curvilinear axis of a macrotidal estuary (theScheldt, BE-NL) as a function of freshwater river discharge Qr. The solid line is the theoretical Qr-S curvefor an estuary at steady state. The thin arrow represents the observed yearly time evolution path. The doublearrows indicate departure from steady state. b Longitudinal distribution of the residual water flow (\ Q [ -Qr) computed at different times of the year for different river discharges.\ Q [ is the tidally averaged waterflux through a given cross section. Modified from Regnier et al. (1998)

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erre

acti

on

s.R

ecta

ng

les

var

iab

les.

Gre

enp

hy

topla

nkto

nan

db

iog

enic

sili

ca;

Yel

low

inorg

anic

nu

trie

nts

;B

row

nd

etri

tal

org

anic

mat

ter;

Blu

ed

isso

lved

gas

es;

Ora

ng

ein

org

anic

carb

on

var

iab

les;

Pu

rple

oth

ersp

ecie

s.W

iggly

arr

ow

sre

pre

sen

tse

ttli

ng

and

dep

osi

tio

n

Aquat Geochem (2013) 19:591–626 601

123

phytoplankton generally suffers from osmotic stress upon exposure to salinity change,

resulting in a characteristic transition from stenohaline freshwater to mesohaline and

euryhaline marine phytoplankton groups along the estuarine salinity gradient (e.g. Lionard

et al. 2005; Muylaert et al. 2009; Lancelot and Muylaert 2011). In polluted estuaries that

are subject to high nutrient loads, turbidity and residence time are the dominant controls on

NPP (Gattuso et al. 1998; Cloern 1999; Desmit et al. 2005; Gazeau et al. 2005; Arndt et al.

2007). An accurate description of NPP therefore requires quantification of the in situ light

availability and phytoplankton growth parameters specific for light-limited systems

(Harding et al. 1986; Langdon 1988; Lancelot et al. 1991, Lewitus and Kana 1995;

Lancelot et al. 2000; Desmit et al. 2005). Estuarine NPP rates determine the relative

contribution of autochthonous organic matter to the estuarine C budget, but also the extent

to which the dissolved inorganic nutrient pools of phosphate (PO43-), nitrogen (DIN = NH4

?

?NO3- ?NO2

-) and silica (H4SiO4) are consumed (Fig. 5). In diatom-dominated estuaries,

subject to high PO43- and DIN loadings, H4SiO4 is often the limiting nutrient and a

complete consumption during the phytoplankton bloom may occur (Arndt et al. 2007). In

addition, NPP fixes dissolved inorganic carbon (DIC), produces oxygen (O2) and impacts

the exchange fluxes of estuarine gases through the air–water interface. It also exerts a

complex influence on the alkalinity (Alk) budgets with opposite effects depending on

whether NH4? or NO3

- is the preferential N source (Table 1).

A fraction of detrital organic matter of variable stoichiometric Redfield ratio is degraded

by microbial activity during estuarine transit, thereby releasing various amounts of inor-

ganic nutrients, DIC and alkalinity (Fig. 5; Table 1). The rate of heterotrophic degradation

strongly depends on the reactivity of the organic matter (Arndt et al. 2013). The complex

mix of allochthonous and autochthonous organic carbon compounds contains myriad

structural motifs and functional groups covering a large range of degradabilities. With the

exception of labile fresh anthropogenic DOC, terrestrial organic matter is generally less

reactive than algal organic matter (e.g. Hedges et al. 2000) due to (i) a chemical com-

position dominated by moderately resistant (e.g. cellulose, lignin and cutin) or highly

resistant (e.g. cutan) biopolymers (de Leeuw and Largeau 1993), (ii) pre-ageing during

burial in soils and subsequent transport and/or (iii) protection via associations with min-

erals or other organic matter (e.g. Bianchi 2011). In addition, deposition/erosion cycles and

redox oscillations characteristic of estuaries (Abril et al. 2000) may induce a repartitioning

of organic matter between particulate and dissolved phases, which affects the composition

and degradability of organic matter (Keil et al. 1997; Hedges and Keil 1999). This com-

plexity in organic matter composition and reactivity is currently poorly represented in

estuarine biogeochemical models and constitutes a serious limitation for diagnostic and

prognostic analyses, especially in poorly surveyed estuarine systems.

Heterotrophic degradation often results in a characteristic redox zonation of the estu-

arine waters (e.g. Billen 1975; Wollast and Peters 1978; Wollast 1983; Regnier et al. 1997;

Eyre and Balls 1999; Eyre 2000; Heip and Herman 1995; Bianchi 2007). In particular, in

estuaries that are subject to high riverine organic matter inputs, high aerobic respiration

rates may exceed the uptake capacity for atmospheric oxygen, resulting in anoxic condi-

tions in some portions of the water column and high denitrification rates (Officer et al.

1984; Paerl et al. 1998; Rabalais and Turner 2001). If nitrate becomes a limiting reactant

for organic matter degradation, other anaerobic pathways such as methanogenesis or

sulphate reduction may be initiated (Thullner et al. 2007). However, these pathways are

generally quantitatively significant only for organic matter degradation in estuarine sedi-

ments where oxygen is rapidly depleted within the first few centimetres (Fig. 5, Pallud and

Van Cappelen 2006). Downstream, an intensification of mixing processes improves water

602 Aquat Geochem (2013) 19:591–626

123

Tab

le1

Sto

ichio

met

ryo

fth

ebio

geo

chem

ical

reac

tions

infl

uen

cing

the

estu

arin

eC

dynam

ics

Rea

ctio

nst

oic

hio

met

ryC

H2O

Ph

yD

ICA

lk

FC

O2

CO

2a

qðÞ$

CO% 2

±1

*0

NP

PN

O3

10

6C

O2þ

12

2H

2Oþ

16

NO� 3þ

HP

O2�

4þ

18

Hþ�!h

tP

hyþ

13

8O

2?

1-

1?

17

/10

6*

*

NP

PN

H4

92

CO

2þ

92

H2Oþ

16

NHþ 4þ

14

HC

O� 3þ

HP

O2�

4�!h

tP

hyþ

10

6O

2?

1-

1-

15

/10

6*

*

Aer

ob

icd

egra

dat

ion

CH

2Oþ

10

6O

2!

92

CO

2þ

14

HC

O� 3þ

16

NHþ 4þ

HP

O2�

4þ

92

H2O

-1

?1

?1

5/1

06

**

Den

itri

fica

tio

nC

H2Oþ

94:4

NO� 3!

55:2

N2þ

92:4

HC

O� 3þ

13:6

CO

2þ

HP

O2�

4þ

84:8

H2O

-1

?1

?9

3.4

/10

6*

*

Nit

rifi

cati

on

NHþ 4þ

2O

2!

NO� 3þ

2Hþþ

H2O

0*

**

-2

**

*

Mo

rtal

ity

Ph

y!

CH

2O

?1

-1

00

All

stoic

hio

met

ric

coef

fici

ents

are

giv

enp

erm

ole

of

Cre

acte

d,

exce

pt

for

the

nit

rifi

cati

on

reac

tio

n.

Ph

yan

dC

H2O

den

ote

liv

ing

ph

yto

pla

nk

ton

and

det

rita

lo

rgan

icm

atte

r,re

spec

tivel

y.

Both

are

assu

med

tohav

eth

est

oic

hio

met

ric

rati

o(C

H2O

) 106

(NH

3) 1

6(H

3P

O4)

*D

epen

ds

on

the

dir

ecti

on

of

the

flu

x(?

:d

isso

luti

on

;-

:outg

assi

ng),

**

assu

min

gR

edfi

eld

stoic

hio

met

ric

rati

o,

***

per

mole

of

Noxid

ized

Aquat Geochem (2013) 19:591–626 603

123

column oxygenation and ultimately results in fully oxic conditions. Nitrification is another

major process in polluted estuaries subject to large ammonium loads originating mainly

from sewage discharge (Billen 1975). It exerts a strong control not only on the O2 balance

and N speciation (Fig. 5), but also on the alkalinity and pH of estuarine waters (e.g.

Regnier et al. 1997; Dai et al. 2006; Hofmann et al. 2008b). Therefore, nitrification needs

to be accounted for in the estuarine greenhouse gas dynamics. The rates of ammonium

oxidation have been extensively studied in the laboratory and in the field (e.g. Billen 1975;

Brion and Billen 1998; Soetaert et al. 2006; Dai et al. 2008) and reveal a complex seasonal

pattern attributed to the growth of the chemoautotrophic bacteria sustaining their metabolic

needs by catalysing this redox reaction.

Gas exchange at the air–estuarine water interface controls not only the dissolved O2

level, but also DIC concentrations and, thus, the entire inorganic carbon system of estuaries

(Fig. 5). The exchange rate is determined by the gas concentration gradient at the interface

(see e.g. Weiss and Price 1980; Benson and Krause 1984) and the piston velocity, which is

a function of the current velocity (O’Connor and Dobbins 1956; Vanderborght et al. 2002;

Borges et al. 2004) and wind speed (Wanninkhof 1992; Raymond and Cole 2001, Regnier

et al. 2002). The respective contribution of these two terms remains nevertheless difficult

to assess (Vanderborght et al. 2002; Alin et al. 2011).

A fraction of the pelagic organic matter is subject to sedimentation and deposition on

the estuarine floor. The benthic degradation of organic matter (Fig. 5) releases DIC,

alkalinity, NH4 and PO4 to the water column. It also drives a downward flux of oxidants

(e.g. O2, NO3, SO4) that are directly consumed either by organic matter degradation or by

re-oxidation reactions of reduced compounds (e.g. Van Cappellen and Wang 1996; Regnier

et al. 2011) produced in situ within the sediments (e.g. NH4, CH4). A fraction of the

deposited organic matter may nevertheless escape decomposition, and sediments are

preferential places for C, N and P burial. Inorganic phosphorus removal can also occur

through sorption and settling of Fe(III) oxides and other solid particles (e.g. Krom and

Berner 1980; Frossard et al. 1995; van der Zee et al. 2007; Spiteri et al. 2008). It can also

remain trapped in the form of highly insoluble Fe-phosphate minerals (Compton et al.

2000; Paytan and McLaughlin 2007).

Similarly, the benthic dissolution of biogenic silica originating from settling of diatom

blooms may represent an important pathway in the estuarine silica cycle (e.g. Struyf et al.

2005). Through mechanisms of physical protection, some of the deposited biogenic silica

can also be preserved in sediments (Qin and Weng 2006). Estuarine sediments could thus

be important modifiers of the fluxes of nutrients from land to ocean (Billen et al. 1991;

Howarth et al. 1995; Tappin 2002). It is, however, important to acknowledge that the

global-scale burial of C, N, P and Si in estuarine systems remains largely unknown

(Rabouille et al. 2001; Laruelle et al. 2009b; Regnier et al. 2013).

3.2.2 Estuarine Biogeochemical Indicators

Biogeochemical indicators are integrative measures of the biogeochemical dynamics.

While most water quality indicators such as nutrient thresholds or the development of toxic

algae blooms only consider specific system attributes, a system-based, holistic approach

relying on a categorization of the estuarine biogeochemical dynamics in terms of NEM,

carbon- and nutrient-filtering capacities and carbon dioxide fluxes (FCO2) is proposed here.

The NEM represents a biogeochemical indicator of the estuarine trophic status (Odum

1956). It is defined as the difference between net primary production (NPP) and total

heterotrophic respiration (HR) on a system scale (e.g. Andersson and Mackenzie 2004). It

604 Aquat Geochem (2013) 19:591–626

123

is therefore controlled by the production and decomposition of autochthonous organic

matter, by the amount and degradability of organic carbon delivered by rivers and by the

export of terrestrial and in situ produced organic matter to the adjacent coastal zone.

Following the definition of NEM, the trophic status of estuaries can be net heterotrophic

(NEM \ 0) when HR exceeds NPP or net autotrophic (NEM [ 0) and when NPP is larger

than HR because the burial and export of autochthonous organic matter exceeds the

decomposition of river-borne material. A recent synthesis by Borges and Abril (2011)

reveals that out of the 79 estuaries investigated, 66 (84 %) have a NEM \ 0. The net

heterotrophic character of estuaries (Fig. 5) is largely related to high allochthonous organic

matter inputs and their high turbidity, which limits NPP despite significant nutrient loads

from the watersheds (Heip and Herman 1995, Gazeau et al. 2004, 2005). Nevertheless,

autotrophic processes progressively gain in importance in downstream direction, and

estuaries become less heterotrophic (Fig. 5). In the coastal ocean, primary production may

exceed respiration and net autotrophy can prevail in this portion of the land–ocean con-

tinuum (e.g. Gattuso et al. 1998; Rabouille et al. 2001; Chen et al. 2003; Ducklow and

McAllister 2004).

The balance between autotrophic and heterotrophic processes controls to a large degree

the inorganic carbon cycle and, thus, the exchange flux of CO2 through the air–water

interface. As detailed in Table 1, biogeochemical processes influence both the dissolved

inorganic carbon (DIC) and alkalinity (Alk) budgets. The resulting speciation of inorganic

carbon species and pH as well as the air–water flux of CO2 can be solved using, e.g. the

standard approach proposed by Follows et al. (2006). These effects are represented

schematically in Fig. 6 for typical estuarine conditions (Zeebe and Wolf-Gladrow 2001).

Aerobic degradation releases significant amounts of DIC but does not change signifi-

cantly the Alk of the water (dAlk/dDIC = 15/106). Therefore, the dDIC and dCO2 induced

by this process are quite similar. Denitrification releases almost as much Alk than DIC

(dAlk/dDIC = 93.4/106) and consequently exerts a marked buffering effect on the CO2

concentration, with a limited change in dCO2 per mole of DIC released. Nitrification

decreases Alk without DIC change and shifts the inorganic carbon speciation towards CO2

(dAlk/dDIC = -2/0). This process leads to a pH drop that favours a CO2 loss towards the

atmosphere. NPP using NO3 as the N source has a higher buffering efficiency than NPP

using NH4, although both pathways promote a pH rise and limit CO2 evasion (Soetaert

et al. 2006). Therefore, the CO2 outgassing can conveniently be decomposed as a sum of

three terms associated with (1) NEM = NPP - HR, (2) the fraction of the CO2 brought

Fig. 6 Effect of biogeochemicalprocesses on DIC and TA. Solidlines indicate levels of constant[CO2] (in mmol m-3), and dottedlines indicate levels of constantpH. Those results are presentedfor a salinity of 15 and atemperature of 17 �C.Stoichiometric equations relatedto each process are given inTable 1

Aquat Geochem (2013) 19:591–626 605

123

into the estuary by supersaturated river waters that is outgassed during estuarine transit and

(3) CO2 produced through a shift in speciation induced by nitrification (Regnier et al. 1997;

Frankignoulle et al. 1998; Vanderborght et al. 2002; Borges and Abril 2011). The NEM

contribution can further be decomposed into its component fluxes (aerobic respiration,

denitrification, NPP).

It should be noted that carbonate precipitation (dAlk/dDIC = -2/-1) and dissolution

(dAlk/dDIC = 2/1) may also influence the inorganic carbon balance, respectively, in

favour and against a CO2 transfer towards the atmosphere. For instance, it has been shown

that the Net Ecosystem Calcification (NEC, defined as the difference between calcification

and carbonate dissolution) contributes to the CO2 evasion of many shallow tropical

estuarine systems where benthic calcification is significant (Andersson and Mackenzie

2004). Nevertheless, it is very likely that the NEM largely dominates the inorganic carbon

balance in most temperate land–ocean transition systems (Borges and Abril 2011).

The estuarine-filtering capacity is another important Estuarine Biogeochemical Indicator

and is a dimensionless number defined as the ratio of the net consumption of a specific

element integrated over the entire estuarine domain during a given time interval to its total

input (e.g. Nixon et al. 1996; Dettman 2001; Arndt et al. 2009; 2011). Reported DIN-filtering

capacities range from values as low as 0.01–0.1 (Nielsen et al. 1995; Nedwell and Trimmer

1996; Nowicki et al. 1997; Trimmer et al. 1998; Mortazavi et al. 2000; Eyre and McKee 2002;

Arndt et al. 2009) to values larger than 0.5 (Seitzinger 1988; Wulff et al. 1990; Boynton et al.

1995). Intermediate conditions, in the range 0.1–0.5, have also been reported (Nixon et al.

1996; van Beusekom and de Jonge 1998; Arndt et al. 2009). The retention of silica in estuaries

has been much less studied, but the few reported filtering capacities range between 0 and 0.4

(DeMaster 1981; Aston 1983; Conley 1997; Arndt et al. 2009). Surprisingly, the estuarine-

filtering capacity with respect to carbon has not been formally investigated.

The filtering capacity is usually defined for a specific element irrespective of its

chemical form, e.g. total carbon made of the sum of inorganic and organic carbon species,

both in the dissolved and in the particulate phases. Using this definition, the long-term

filtering capacity (annual to decadal timescales) can then be attributed to the exchange of

matter through the material surfaces of the estuary (loss to the air by outgassing or loss

through burial). On shorter, seasonal timescales, the filtering capacity may also be influ-

enced by transient mass accumulations within the estuary (e.g. Regnier and Steefel 1999;

Arndt et al. 2009).

4 Quantifying the Estuarine Filter

4.1 Data-Driven Approaches and Box Models

Property-salinity plots have been widely used to estimate the export fluxes of carbon and

nutrients from estuarine systems (see e.g. Stommel 1953; Ketchum 1955; Boyle et al.

1974; Pritchard 1974; Liss 1976; Wollast and Peters 1978; Officer 1980; Kaul and Froelich

1984; Mills and Quinn 1984; Billen et al. 1985; Keeney-Kennicutt and Presley 1986;

GESAMP 1987; Yeats 1993; Shiller 1996; Cai and Wang 1998; Cai et al. 2004). This so-

called apparent zero end-member (AZE) method builds on the assumption that mixing two

water masses of different salinities results in a linear distribution of conservative species

along the salinity gradient (e.g. Boyle et al. 1974; Officer and Lynch 1981). Based on this

assumption, net export fluxes can then be calculated by extrapolating concentrations

measured in the saline part of the estuary to the point of zero salinity. The intercept of the

606 Aquat Geochem (2013) 19:591–626

123

regression (the apparent zero end-member concentration, AZE) multiplied by the river

discharge gives an estimate of the export flux for a reactive constituent. Estimates derived

using the AZE method can only account for biogeochemical transformations within the

saline part of the estuary and, therefore, ignore any processing taking place in the tidal

river (Vanderborght et al. 2002; Amann et al. 2012). Numerous studies have also high-

lighted that the AZE technique introduces large errors in the estimation of the long-term

residual constituent flux towards the coastal zone (e.g. Boyle et al. 1974; Officer and Lynch

1981; Kaul and Froelich 1984; Regnier et al. 1998; Webster et al. 2000). However, the

most important impediment to its application is the inherently transient nature of estuarine

systems that results in nonlinear mixing curves (see Sect. 3.1). This limitation applies to

the full spectrum of estuaries, from those having short residence times of days to those

exhibiting much longer residence times of weeks to months.

Box models have been used as an alternative approach, amenable for non-steady-state

conditions (Schroeder 1997; Garnier et al. 2008; Wulff et al. 2011). Box models treat the

estuary as a single, vertically and horizontally well-mixed box with steady residual

hydrodynamic characteristics. The use of box models to quantify carbon and nutrient

cycling in estuarine systems was made particularly popular by the LOICZ program

(Gordon et al. 1996). However, studies have shown that the use of time-averaged con-

centrations, the assumptions of a well-mixed box and steady-state residual flow may result

in large errors in estimates of estuarine transformation rates and export fluxes (e.g. Regnier

et al. 1998; Webster et al. 2000; Arndt et al. 2009). For instance, Webster et al. (2000)

showed that internal production from a distributed source is underestimated by a factor of

two if the estuary is treated as a well-mixed box. In general, the errors depend on estuary’s

mixing and geometrical characteristic as well as on the location of the source. The box

model approach is also very difficult to apply to estuaries characterized by high average

salinities, because it scales the net export to a horizontal gradient that is highly uncertain.

Therefore, reliable carbon and nutrient flux estimates call for methods that can account for

the strong spatial and temporal variability of the estuarine environment.

4.2 Reaction-Transport Models

4.2.1 Spatial–Temporal Variability: Models as Integration Tools

RTMs are, in combination with observational data, ideal tools to investigate and quantify

process rates, material fluxes and budgets at spatial and temporal scales that are not readily

accessible through observations.

As an example, Fig. 7 illustrates the simulated annual evolution of the NEM in a macro-

tidal estuary. A quantitative assessment of this annual evolution would be difficult, if not

impossible, on the basis of observations alone, since the NEM is an integrative measure of

the whole system biogeochemical dynamics and reveals a significant temporal variability

ranging from the hourly to the seasonal timescale (Fig. 7). It is thus not a directly

observable quantity. Simulation results show that the NEM is negative throughout most of

the year, reflecting the dominant contribution of heterotrophic processes, a common

characteristic feature of many estuarine environments (Borges and Abril 2011). In par-

ticular, during winter, high heterotrophic process rates are sustained by large inputs of

allochthonous organic material. During the summer months, an increase in ambient tem-

perature supports high heterotrophic rates and maintains a mean, negative NEM. However,

a simultaneous increase in primary productivity leads to a complex balance between

autotrophic and heterotrophic processes that is reflected in large, short-term NEM

Aquat Geochem (2013) 19:591–626 607

123

fluctuations. The estuary may even become net autotrophic (NEM [ 0) when low SPM

concentrations in combination with high solar radiation increase the in situ light avail-

ability and, thus, promote high net primary production rates that exceed heterotrophic

degradation rates.

Similar to the NEM, estuarine mass inventories and export fluxes are spatially inte-

grative measures of a complex process interplay (Arndt et al. 2009, 2011). In particular, the

estuarine–coastal ocean interface is characterized by instantaneous fluxes that are orders of

magnitude larger than the residual flux and comprise a strong dispersive component flux

(Regnier and Steefel 1999; Arndt et al. 2011). Therefore, the quantification of carbon and

nutrients export is hardly achievable with observational means alone.

Figure 8 illustrates the simulated annual evolution of the estuarine silica mass budget in

a macro-tidal estuary (Arndt et al. 2009). It shows the residual silica input and output fluxes

across the estuarine interfaces (Fig. 8a, d, respectively), the mass of silica within the

estuary (Fig. 8b), and the spatially integrated consumption rate of silica (Fig. 8c). The

large intra-annual variability in the silica inventory and flux is an incitement to establish an

estuarine silica budget at the biogeochemically relevant seasonal timescale (Fig. 8e).

Simulation results highlight the transient nature of the silica dynamics and the critical role

of changes in the silica mass inventory. Large seasonal changes (Fig. 8b) are caused by the

transient nature of the mass transport, as well as by the nonlinearity in instantaneous and

residual flows (see Sect. 3.1). In winter and autumn, high discharge periods trigger an

increase in the storage of silica within the estuary (Fig. 8a, b). The stored silica is then

progressively released during spring and summer, resulting in a depletion of the estuarine

silica inventory (Fig. 8b, e). In addition, silica consumption further depletes the silica pool

in summer (Fig. 8c, e). As a consequence, the filtering capacity of the system increases

from close to zero in winter to 0.81 in summer. The build-up of the silica inventory and its

delayed release has important implication for silica export fluxes to the coastal ocean. In

particular, the export flux is characterized by a damped and smeared response to the winter

fluctuations in input flux, resulting in a significant imbalance between input and output

fluxes (Fig. 8d).

The quantitative assessment of the estuarine carbon and nutrient fluxes is further

complicated by the complex interplay of estuarine and coastal processes at the transition

between these two environments (e.g. Arndt et al. 2011). Because the separation between

estuarine and coastal research has largely been based on the geographical criteria, estuarine

models have generally neglected the marine influence. A fully transient simulation of the

entire mixing zone of the estuary–coastal zone continuum of the Scheldt (Arndt et al. 2011)

suggests nevertheless that the estuarine–coastal zone interface may play a significant role

Fig. 7 Annual evolution of theNEM for an entire macro-tidalestuary and tidal river (theScheldt, BE-NL)

608 Aquat Geochem (2013) 19:591–626

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in the biogeochemical dynamics (Fig. 9). In this transition zone, marked spatial concen-

tration gradients develop and episodically lead to a reversal of material fluxes from the

coast into the estuary (Arndt et al. 2011). During distinct episodes of the productive period,

euryhaline coastal diatoms intrude far upstream into the saline estuary (Fig. 9), creating a

strong CO2 sink close to the estuarine mouth (Gypens et al. 2011). The diatom intrusion

reduces the estuarine nutrient concentrations and export fluxes, thereby reinforcing the

nutrient limitation in the coastal area. As a consequence, the estuarine filter does not

operate independently from the processes in the coastal zone. The dynamic interplay

Fig. 8 Annual evolution of a dissolved silica budget. a riverine influx, b change in inventory, c silicaconsumption over the entire estuary, d residual export flux through estuarine mouth, e seasonally resolvedestuarine budget. Each contribution is scaled to the yearly integrated riverine influx (820 106 mol). Modifiedfrom Arndt et al. (2009)

Fig. 9 Intrusion of a marinediatom bloom in an estuary–coastal zone continuum. Thesymbols represent the migrationof the location where maximumbiomass is simulated (from Arndtet al. 2011)

Aquat Geochem (2013) 19:591–626 609

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between the two ecosystems and the intense process rates operating at their transition,

therefore, strongly support a continuum approach.

4.2.2 Disentangling the Biogeochemical Complexity: Models as Diagnostic Tools

RTMs can be used to disentangle the complex biogeochemical process interplay that

underlies system-wide biogeochemical indicators, such as NEM (e.g. Volta et al. 2013),

carbon and nutrient budgets (e.g. Soetaert and Herman 1995; Vanderborght et al. 2002),

filtering capacities (e.g. Arndt et al. 2009) or air–water CO2 fluxes (Vanderborght et al.

2002; Hofmann et al. 2008a). For instance, a quantitative assessment of the air–estuarine

water CO2 flux requires a consideration of all transport and reaction processes affecting

estuarine DIC, Alk and pH (see Sects. 3.1, 3.2), as well as temperature and ionic strength

effects on the dissociation constants of carbonate ions (Moek and Koene 1975; Cai and

Wang 1998; Regnier et al. 1997; Hofmann et al. 2008b).

To the best of our knowledge, published modelling studies dedicated to estuarine CO2

dynamics remain limited to the Scheldt estuary. Figure 10 compares RTM simulation

results of pH, partial pressure of CO2 (pCO2) and FCO2 (Vanderborght et al. 2002) with

field observations from this highly heterotrophic system. The longitudinal profile of pH

exhibits a characteristic minimum at low salinity, which is mainly a consequence of

Fig. 10 Comparison ofmodelled and observed inorganiccarbon dynamics along thelongitudinal axis of a macro-tidalestuary (the Scheldt, BE-NL)a pH, b CO2 partial pressure(pCO2), c CO2 efflux. Modifiedfrom Vanderborght et al. 2002

610 Aquat Geochem (2013) 19:591–626

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nitrification and, to a smaller extent, heterotrophic degradation and thermodynamic effects

(Moek and Koene 1975; Frankignoulle et al. 1996; Regnier et al. 1997). The combined

effects of CO2-enriched river water, in situ degradation of organic matter and low pH,

maintain pCO2 values well above equilibrium with the atmosphere over the entire estuary.

The RTM allows computing the daily-integrated CO2 evasion fluxes driven by wind and

currents and indicates that the estuarine system emits more than 200 tons of carbon per day

(Vanderborght et al. 2002). Model results are compared to observed pH and pCO2, as well

as direct flux measurements performed using floating chambers (Frankignoulle et al. 1998),

and the overall consistency between simulation results and observations can be considered

as a robust test for the model. In particular, the estuarine pH is highly sensitive to many

reaction processes and is thus a very good indicator of the model’s ability to resolve the

underlying biogeochemical dynamics. Small differences between measured and simulated

FCO2 fluxes likely result from the imperfect quantification of piston velocity in estuarine

water.

The quantitative contribution of each biogeochemical process to variations in CO2

concentration (and thus FCO2) can be quantified through their respective effect on the

change in DIC and Alk (Table 1). The rate of change in CO2 concentration due to a given

reaction (dCO2/dt|reaction) is calculated using an expression, which takes into account the

buffering capacity of an ionic solution (e.g. Zeebe and Wolf-Gladrow 2001):

dCO2=dtjreaction¼dDIC=dtjreaction

Ds

� Dh

Ds

dAlk=dtjreaction

Ah

� �= 1� Dh

Ds

As

Ah

� �ð1Þ

where DS and As are the partial derivatives of DIC and Alk with respect to the CO2

concentration at constant pH, respectively, and Dh and Ah are the partial derivatives of DIC

and Alk with respect to pH at constant CO2 concentration. Formulations and a detailed

derivation for these partial derivatives are provided in Zeebe and Wolf-Gladrow (2001).

For the CO2 exchange flux, Eq. 1 reduces to the widely known Revelle equation (Revelle

and Suess 1957) because alkalinity is constant. The above equation can be solved, for each

process, at any given time and location. This approach allows quantifying the effect of

individual biogeochemical processes on the CO2 dynamics but ignores the comparatively

smaller CO2 changes due to advection and mixing (Hofmann et al. 2008b).

Here, the approach is used to quantify the relative contribution of different processes to

the CO2 dynamics in an idealized, funnel-shaped estuary for typical summer conditions

representative of a temperate, Western European climate (Table 2). The RTM approach

follows that of Regnier et al. (1997), Regnier and Steefel, (1999) and Vanderborght et al.

(2002), but the model relies here on idealized geometries and generalized forcing condi-

tions. In short, climate and hydrological forcings are extracted from monthly mean values

for water temperature (World Ocean Atlas, http://www.nodc.noaa.gov/OC5/indprod.html),

mean daily irradiance and photoperiods (Brock 1981), monthly averaged freshwater dis-

charge (Fekete et al. 2002, 2010), and mean daily wind speed (CCMP project; Atlas et al.

2011). These forcings, derived from global databases, are available at a minimum reso-

lution of 1� (Table 2). Water elevations at the estuarine mouth account for the dominant

semi-diurnal tidal component M2 with a constant tidal amplitude. The riverine inputs of

carbon, nutrients and suspended particular matter (Table 3) are extracted from the global

statistical model GlobalNEWS2 (Mayorga et al. 2010) and the Glorich database (Hartmann

et al. 2011). Values represent a mean over all Western European watersheds that discharge

through a tidal estuary (type 2 in the typology of Durr et al. 2011). The lower boundary is

located 20 km beyond the estuary mouth to minimize the marine influence (Table 3). The

Aquat Geochem (2013) 19:591–626 611

123

parameter values of the biogeochemical reaction network and sediment parameters are

adopted from Arndt et al. (2009) and Volta et al. (2013), respectively. These values are

broadly consistent to other estimates reported for other tidal estuaries in Western Europe

(Table in Online Resource).

Model results highlight the dominance of aerobic degradation in the total estuarine CO2

production (*60 %). Denitrification plays, because of its low rates and strong buffering

capacity, a much smaller role in total estuarine CO2 production (*1 %). Nitrification

exerts a significant influence on the CO2 production and outgassing (*25 %) because it

decreases Alk, lowers pH and, thus, shifts the equilibrium of DIC species towards CO2.

NPP generally promotes CO2 uptake but is of minor significance (*-5 %), due to the

heterotrophic character of the simulated estuarine system. CO2 outgassing decreases DIC

without changing the alkalinity and hence promotes proton and CO2 consumption, which

counteracts its evasion. Overall, the CO2 exchange through the air–water interface partly

buffers the decrease in pH attributed to heterotrophic degradation and nitrification. The net

rate of change in CO2 (bold line in Fig. 11) indicates that the CO2 concentration decreases

all along the estuary, because the CO2 outgassing exceeds its production by heterotrophic

degradation and nitrification. In addition, the simulated spatially integrated DIC loss by

outgassing (FCO2) exceeds the production of DIC by NEM (Fig 11, inset). This result

indicates that, in addition to nitrification (*25 %), another source largely attributable to

the input of inorganic carbon from the river must contribute to the estuarine outgassing

Table 2 Climate forcings representative of temperate Western Europe used to constrain our simulations

Forcings Value Database spatial resolution

Water temperature (�C) 18 1�Windspeed (m s-1) 2 0.25�Mean solar radiation (lE m-2 s-1) 750 –

Photoperiod (h) 17 –

Table 3 Boundary conditions for biogeochemistry corresponding to the different simulations described inthe text

REF POL (1–2) PRIS (1–2) Estuarine mouth

DIN (mmol m-3) 150 800 50 25

NH4/DIN 0.15 0.6 0.3 0.1

TOC (mmol m-3) 500 1000 300 0

Si (mmol m-3) 100 100 100 10

TSS (gr l-1) 0.07 0.07 0.07 0.03

O2 (mmol m-3) 200 100 300 220

P (mmol m-3) 7.5 10 5 0.1

DIC (mmol m-3) 3,160 3170–3375 3,045–2,837.5 2,209.8

ALK (mmol m-3) 3,000 3,000 3,000 2,476.4

pCO2 (latm) 4,205 5,000–9,000 2,000–367 367

pH 7.39 7.32–7.07 7.7–8.4 8.2

NB: ALK is constant, and pCO2 is fixed. Other variables for the carbonate system are determined usingthose two values

612 Aquat Geochem (2013) 19:591–626

123

(*20 %). Such dynamics are supported by observations from rivers in the South-eastern

USA, where high pCO2 and large FCO2 result from allochthonous inputs from tidally

flooded salt marshes and groundwater (e.g. Cai and Wang 1998; Cai et al. 1999; Cai 2011).

4.3 Exploring Trends in Estuarine Biogeochemical Dynamics at Regional and Global

Scales

The previous sections presented several examples of RTM applications to quantify and

disentangle the complex process interplay that underlies the biogeochemical dynamics,

air–water CO2 fluxes and NEM along river–estuary–coastal zone continua at the local

scale. However, RTMs can also be used to systematically explore the estuarine biogeo-

chemical dynamics in a more general framework over a range of different, idealized

estuarine geometries and a number of different environmental scenarios.

Here, we analyse the response of the biogeochemical indicators FCO2, NEM and total

C-filtering capacities to changes in estuarine geometry (funnel-shaped, mixed and pris-

matic; Table 4) for different environmental scenarios (polluted, reference and pristine;

Table 5), again assuming typical Western European summer conditions. Steady-state

simulations are performed for each estuarine geometry and environmental scenario. RTM

simulations for the funnel-shaped estuary under reference conditions are already presented

in Fig. 11 and discussed in Sect. 4.2.2.

Figure 12 a–d shows the longitudinal profiles of total heterotrophic degradation, nitri-

fication and FCO2 for the funnel-shaped and prismatic geometries under reference con-

ditions for the set of kinetic constants reported in the literature (BASE). The sensitivity of

these processes to changes in the interaction timescales between transport and biogeo-

chemical processes is also shown, using rate constants for degradation and nitrification that

are one order of magnitude smaller (SLOW). In addition, the response of biogeochemical

reaction rates and FCO2 to an increase in organic carbon, nutrient (Fig. 12e, f) and inor-

ganic carbon (Fig. 12f) inputs (polluted scenario) is illustrated for the case of the funnel-

shaped estuary.

Despite their very different geometries and, thus, hydrodynamic characteristics and

residence times (Fig. 3), the funnel-shaped and prismatic estuaries reveal similar longi-

tudinal rate and flux profiles (Fig. 12a–d). The highest reaction rates and FCO2 are

Fig. 11 Contribution of individual biogeochemical processes to estuarine atmosphere CO2 flux for anidealized, funnel-shaped estuary. Positive values denote outgassing. Thin lines: a: aerobic degradation, b:nitrification, c: denitrification, d: NPP, e: gas dissolution. Thick line: net exchange rate. The inset shows theestuarine-integrated air–water CO2 outgassing (FCO2) and the NEM

Aquat Geochem (2013) 19:591–626 613

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simulated in the upper estuarine reaches. Both rates and fluxes decrease downstream as a

consequence of organic matter and ammonium consumption by biogeochemical processes

and dilution with seawater. In the funnel-shaped estuary, the rates become very low around

70 km and indicate that, due to the long residence time (*70 days), organic matter and

ammonium are almost completely consumed in the upper estuarine reaches. The resulting

decrease in reaction rates leads to a sharp decrease in FCO2 in the same area. In the

prismatic estuary, the shorter residence time (*8 days) is responsible for a slight down-

stream movement of the reaction front, which extends the reaction zone by about

10–20 km. Low reaction rates are nevertheless simulated in the lower estuary, indicating

that the reduced species CH2O (and ammonium) are also efficiently oxidized within the

prismatic estuarine system. As a consequence, both estuaries are characterized by similar

C-filtering capacities (Table 5).

A tenfold decrease in the rate constants for biogeochemical processes results in largely

different longitudinal reaction rate profiles (Fig. 12a–d). In the funnel-shaped estuary,

however, the reduction in reaction rate constants merely triggers an expansion of the

organic matter degradation and nitrification zone by about 50 km (Fig. 12a), indicating

that the long residence time of the system still allows for a complete consumption of the

reactive species. In the prismatic estuary, on the other hand, the biogeochemical rates

remain almost constant along the estuarine gradient (Fig. 12c). Here, the reduction in the

rate constants increases the relative importance of the advective transport, which triggers a

large export of organic matter (and ammonium) to the adjacent coastal ocean. In both

estuaries, FCO2 longitudinal profiles exhibit a rapid decrease due to the outgassing of

saturated riverine waters to much lower values, resulting from a delicate balance between

primary production (not shown) and the now reduced degradation and nitrification rates.

Table 4 Generic estuarine geometries and corresponding hydrodynamic parameters

Funnel shaped Mixed Prismatic

Length (km) 150 150 150

Width convergence length (km) 30 70 150

Depth (m) 7 7 7

Width at the mouth (km) 10 5 3

Discharge (m3/s) Q - (50) Q ref (100) Q ?? (300)

Tidal amplitude (M2) (m) 3.7 3 2.5

Table 5 Total C-filtering capacities expressed as percentage of the total riverine input for the baselineparametrization (BASE) and low kinetic constants parametrization (SLOW) for each estuarine geometry

Funnel shaped Mixed Prismatic

BASE SLOW BASE SLOW BASE SLOW

Ref. 31.3 28.3 29.6 22.5 25.0 10.2

POL1 58.3 52.1 57.6 41.4 52.8 20.2

POL2 60.7 54.7 61.0 45.6 56.0 25.0

PRIS1 23.5 21.8 21.1 17.2 16.5 7.2

PRIS2 18.9 16.6 16.9 11.3 11.9 1.1

614 Aquat Geochem (2013) 19:591–626

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Overall, however, the C-filtering capacity of the prismatic estuary is much more sensitive

(60 % decrease) to changes in reaction constants than the filtering capacity of the funnel-

shaped system (10 % decrease). Simulation results thus emphasize the importance of the

interaction timescales between biogeochemical and transport processes and, hence,

between estuarine biogeochemistry and geometry.

Heavily polluted estuaries generally receive large ammonium and highly variable C

loads. Therefore, riverine pollution may exert an important influence on the balance

between heterotrophic degradation processes and nitrification, with potential implications

for FCO2. Fig. 12e, f illustrates the effect of pollution (increased organic carbon and

ammonium loads) on total heterotrophic degradation and nitrification rates, as well as on

estuarine CO2 fluxes in the funnel-shaped estuary. Maximum degradation rates (Fig. 12e)

remain similar to those predicted for the reference case (reflecting zero-order kinetics with

respect to organic matter), but the zone of degradation expands by about *25 km towards

the mouth. Overall, the effect of this process on FCO2 is moderate (Fig. 12f). Intense

nitrification results in a pH decrease which triggers much higher FCO2 (Fig. 12f) than in

the reference case (Fig. 12a). The C-filtering capacities are thus significantly larger

(Table 5) and are dominated by nitrification (see also Sect. 4.2.2). In the upper estuarine

reaches, the pH drop due to nitrification leads to an initial increase in FCO2, despite

decreasing DIC concentrations (Fig. 12f). Further downstream, FCO2 decreases in

response to the downstream decrease in biogeochemical reaction rates and pCO2, but the

outgassing remains higher than in the reference case. An additional increase in riverine

pCO2 (larger DIC with constant alkalinity) supports an even larger outgassing fluxes within

Fig. 12 Longitudinal profiles of total heterotrophic degradation (TH, aerobic degradation ? nitrification)and nitrification rates (NIT), and corresponding FCO2 along the estuarine gradient of a funnel-shapedestuary (a, b) and a prismatic estuary (c, d). SLOW indicates that organic matter degradation andnitrification kinetic constants are divided by 10 compared to BASE parameterization. e and f illustrates theeffects of highly polluted systems (see Table 3 for description of the two pollution scenarios) on rates andfluxes for the funnel-shaped estuary

Aquat Geochem (2013) 19:591–626 615

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the upper reaches (Fig. 12f) and, thus slightly higher C-filtering capacities (Table 5).

Nevertheless, FCO2 becomes similar for both pollution scenarios within a distance of circa

50 km, once most of the riverine supersaturated waters have outgassed within the estuary.

Table 5 complements the results shown in Fig. 12 and summarizes the results of our

prognostic analysis of C-filtering capacities computed for all the estuarine types (funnel-

shaped, mixed and prismatic) and environmental scenarios (pristine to heavily polluted

conditions, Table 3). For all estuarine types, the C-filtering capacity increases from pristine

to polluted conditions due to the increasing influence of nitrification on pH and CO2

dynamics. Furthermore, the C-filtering capacity generally decreases with residence time,

from funnel-shaped to mixed and then to prismatic estuarine types. Nevertheless, the effect

of estuarine geometry and hydrodynamics strongly depends on the interaction timescales

between biogeochemical reaction and transport processes. For the parameterization set

using literature values, differences in filtering capacities across the different estuarine types

do not exceed 10 %. However, the importance of estuarine geometry increases with the

tenfold reduction in kinetic rate constants. Overall, lower kinetic constants induce sig-

nificantly lower filtering capacities, but the relative decrease and its sensitivity to different

environmental scenarios is much larger ([50 %) in the prismatic estuary than in the mixed

(20–40 %) and funnel-shaped estuaries (\15 %) due to the short residence time (Table 5).

Figure 13 shows the relationship between estuarine FCO2 and NEM for the three dif-

ferent estuarine geometries and the environmental scenarios analysed. Simulated FCO2 and

NEM fall within the range of globally observed values summarized by Laruelle et al. (2013)

with mean values of 21.9 and -11.0 mol C m-2 year-1, respectively. Simulation results

show that for the reference conditions, the estuarine FCO2 is mainly driven by heterotrophic

processes and shows a strong linear correlation with NEM, in agreement with the results of

Maher and Eyre (2012). The absolute magnitude of NEM and FCO2 decrease from pris-

matic to mixed and to funnel-shaped because these variables correlate with the input fluxes

and, thus, to the river discharges across estuarine types (Table 4). Figure 13 also shows that

environmental conditions exert an important influence on the relationship between NEM

and FCO2. Under pristine conditions, the slope of the linear regression is steeper than under

reference and polluted conditions. These findings emphasize that NEM is an important

driver of FCO2 in pristine systems. However, in polluted estuaries, the nitrification rates

become increasingly more important and eventually support more than 50 % of the total

CO2 flux in the polluted scenario. In addition, higher riverine pCO2 in the polluted scenario

decreases further the slope of the regression lines, indicating that the contribution of

supersaturated riverine waters becomes more important in the FCO2 budget.

Fig. 13 NEM as a function of mean annual FCO2 under pristine (PRIS 1 and PRIS 2, a), reference (REF, b)and polluted (POL 1 and POL 2, c) conditions (see Table 3). Circles, triangles and squares represent funnel-shaped, mixed-type and prismatic estuaries, respectively. The linear regression between NEM and FCO2 isindicated for PRIS 1, REF and POL 1

616 Aquat Geochem (2013) 19:591–626

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These results, albeit relying on a limited number of end-member cases, already high-

light that the quantification of crucial biogeochemical processes and fluxes such as the

FCO2 results from a complex combination of factors, which can be identified and disen-

tangled using RTMs with generic geometries and forcing conditions. Such a generic

approach reduces data requirements and is numerically cost-efficient, but at the same time

maintains the physical and biogeochemical complexity required to quantify estuarine

biogeochemical dynamics (see Sects. 3.1, 3.2). Furthermore, it provides an objective,

rational framework in which alternative simplification hypothesis and directions for

meaningful upscaling strategies can be tested. In addition, the model approach can be

combined with continuously growing global, high-resolution climatological, hydrological

and environmental databases such as those used to design environmental scenarios for the

presented set of prognostic RTM simulations. This combination offers promising avenues

to assess the quantitative contribution of estuaries to global biogeochemical cycles and the

response to climate change using mechanistically rooted upscaling strategies.

5 Conclusion and Outlook

Over the past few decades, increasingly complex reaction-transport modelling approaches

have been applied to disentangle the interplay of physical, geochemical and biological

processes that controls estuarine biogeochemical dynamics. These efforts have helped

establish carbon and nutrient budgets and fluxes for many well-surveyed estuaries, at ever-

increasing spatial and temporal resolution. Although clearly biased towards systems in

industrialized countries, the modelling studies reveal that the estuarine bioreactor exerts a

significant influence on land–ocean fluxes and is a relevant contributor to the atmospheric

CO2 budget. Yet, despite this widely recognized role, the global significance of estuaries

for elemental cycles and climate remains frought with large uncertainties. This lack of

quantitative understanding can be attributed mainly to the prohibitive computational cost

required to simulate estuarine biogeochemical dynamics at the appropriate temporal and

spatial scales, as well as the limited availability of comprehensive data sets that resolve the

diversity of estuarine environments. Therefore, one of the biggest future challenges in

estuarine biogeochemical research will be to develop suitable quantitative approaches that

allow assessing the role of the estuarine biogeochemical reactor for global biogeochemical

cycles and climate, as well as its response to climate and land-use changes at both a global

scale and over climate relevant timescales. Here, we illustrated a data model approach that

opens promising avenues in this direction, but also calls for:

• Comprehensive and Comparative Data Sets

The need for regionalization is evident because important controls of estuarine bio-

geochemical dynamics, such as temperature, watershed characteristics, organic matter

inputs or pollution, vary geographically. Detailed local studies form the basis for the

identification of global patterns. However, existing data sets are largely biased towards

industrialized countries, while observations remain scarce for other regions. Future mon-

itoring efforts should thus be strategically co-ordinated to fill these knowledge gaps.

• Continuum Approaches in Estuarine Research

A comprehensive assessment of the estuarine biogeochemical dynamics necessitates a

continuum representation of the land–ocean interface, from the catchment to the coastal

Aquat Geochem (2013) 19:591–626 617

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zone. This is especially critical for reconstructing and forecasting the response of the

estuarine filter to changes in land-use and climate.

• Integration Within Earth System Models

Earth system models (ESM) designed to study the coupled carbon cycle and climate

lack an explicit representation of estuarine systems, mainly because of computational

constraints. Therefore, upscaling strategies that allow incorporating the estuarine filter in

ESMs at low computational costs need to be developed, in particular to separate the natural

and anthropogenic contributions to the global estuarine carbon fluxes and their future

response to climate and environmental change.

Our ability to understand the role of the land–ocean continuum for global biogeo-

chemical cycles and climate will critically depend on a better quantitative understanding of

the estuarine biogeochemical dynamics on a global scale.

Acknowledgments This manuscript has greatly benefited from insightful comments from Wei-Jun Caiand the editorial work of Eric De Carlo. The research leading to these results has received funding from thegovernment of the Brussels-Capital Region (Brains Back to Brussels award to P. Regnier), by the EuropeanUnion’s Seventh Framework Program (FP7/2007-2013) under Grant Agreement No. 283080, projectGEOCARBON, by the German Science Foundation DFG (DFG-project HA 4472/6-1) and the Cluster ofExcellence ‘‘CliSAP’’ (DFG, EXC177), Universitat Hamburg. S. Arndt acknowledges funding by theNational Environmental Research Council (NERC; Grant Number NE/I021322/1), N. Goossens is funded bya FRIA (Fonds de la Recherche Scientifique-FNRS) Grant.

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